Causal manifold

Locally, Minkowski and universal space are identical as causal manifolds, but the universal time is not equivalent to the time registered in the local Minkowski frame. Quantum mechanically temporal evolution and energy are defined by conjugate operators. The operator —i d/dt), which defines the energy (or frequency) depends on the geometry of the stationary state. 

The aims of causality assessment are manifold. Adverse events need to be classified, a decision needs to be made whether a drug has caused this event, regulatory requirements need to be satisfied, signal recognition can be aided, and finally, at the end of this process, a label change may be necessary. 

The early time evolution of I>(t) often is understandable in terms of a causal mechanism where does the system start out, where does it go next, how fast, and why However, the long-time behavior of d (i) typically is understandable only in a statistical sense irreversible decay into a dense manifold of essentially indistinguishable states, describable only in a Fermi Golden Rule sense in terms of (HgD) and po where (H D) is the average squared coupling matrix element between the bright state and the isoenergetic dark states and p is the density of dark states. 

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